Preheat oven to 375°. Toss mushroom slices in 1 tablespoon olive oil and transfer to a baking dish. Bake about 45 minutes until mushrooms are tender. Drain off excess liquid partway through. Drain off any excess liquid when mushrooms are done. Reduce oven to 350°.
Heat remaining tablespoon oil in a large skillet. Add onions and sauté about 8 minutes. Add ground beef and brown over medium high heat. Add rosemary, thyme, salt and pepper to the skillet. Combine beef and mushrooms and set aside.
Heat milk, broth, bay leaf and garlic to a simmer. Remove from heat and allow mixture to stand at least 10 minutes.
Melt butter in a large skillet over medium high heat. Whisk in flour and cook about 2 minutes. Slowly add the hot milk, whisking constantly. Reduce heat to low and simmer about 5 minutes. Remove from heat and add Gruyère cheese, ⅓ cup Parmesan and nutmeg. Set sauce aside.
Bring a large pot of salted water to a boil. Add lasagna noodles and cook according to package instructions. You can reduce cook time by a couple of minutes since noodles will finish cooking in the oven. Drain noodles and rinse with cold water.
Spray a deep 13 X 9" baking dish with cooking spray. Spread 1 ½ cups of sauce over bottom of baking dish. Arrange ⅓ of noodles to cover the bottom of the baking dish. Top noodle layer with ⅓ remaining sauce. Layer half the beef/mushroom mixture over the sauce. Arrange another layer of noodles, half the remaining sauce and the remaining beef/mushroom mixture. Top with the last layer of noodles and remaining sauce. Spread the 1 ½ cups of Parmesan evenly over top of the casserole.
Cover the lasagna with foil. Bake 40 minutes, then remove the foil and bake a further 20 minutes till top is golden brown and sauce is bubbling.
Let lasagna stand 15-20 minutes before cutting and serving.